Spatial Functions

Pre-requisites:

Intro to Spatial Data
Data Formatting

Objectives:

Recognize a few spatial relationships
Understand how to clip a raster

Exercise: Spatial functions with rasters

Relational Operations

Relational operators are a set of methods used to test for the existence of a specified toplogical spatial relationship between two geometric objects as they would be represented on a map. The basic approach to comparing two geometric objects is to project the objects onto the 2D horizontal coordinate reference system representing the Earth’s surface, and then make pair-wise test of the intersections between the interiors, boundaries and exteriors of the twp projections and to classify the map relationship between the two geometric objects based on the entries in the resulting 3 by 3 intersection matrix.[^1]

	Interior	Boundary	Exterior
Interior	dim[{{{1}}}] = 2	dim[{{{1}}}] = 1	dim[{{{1}}}] = 2
Boundary	dim[{{{1}}}] = 1	dim[{{{1}}}] = 0	dim[{{{1}}}] = 1
Exterior	dim[{{{1}}}] = 2	dim[{{{1}}}] = 1	dim[{{{1}}}] = 2

Spatial Predicates

The above figure demonstrates the criteria outlined by the Dimensionally Extended Nine-Intersection Model(DE-9IM). The matrix is used to outline specific spatial relationships or predicates which are more accessible to interpretaion. These named spatial predicates are also used by spatial queries to selet subsets of geometrys that fit in one spatial predicate.

Here is a quick outline of the Spatial Predicates

Equals: The two geometric objects are spatially equal meaning, they represent the same geometry (congruent in geometric terms)
Disjoint: The two geometric objects share no points in common, the two objects are completely separate
Intersects: The two geometric objects have at least one point in common
Touches: The two geometric objects have at least one boundary point in common, but no interior points
Crosses: The two geometric objects share some but not all interior points
Contains: One geometry is contained by the other if all the points of one geometry are within the boundary or interior of the other and they share at least one interior point. This means that this predicate may produce unpredictable behavior for linestrings and points which have no interior points.[^2]
Within: The inverse of Contains. The first geometry is completely within the second geometry
Overlaps: The two geometries share some but not all points in common, the two geometries have the same dimensions and the intersection of the two geometries has the same dimension as the two input geometries
Covers: Similar to contains, but does not require that the two geometries share an interior point, which makes it the proper tool for working with inputs of different dimensions.

Methods for Spatial Analysis

There are a few standard methods for geometric analysis available based on the geoetric object model. This is a brief listing of basic analyses and is by no means exhaustive of the available functions.

Distance: Measures the shortest distance between two geometries.
Buffer: Creates a geometric object that represents all points within a given distance from the given geometry
Convex Hull: Creates a geometric object that represent the minimum bounding convex polygon that contains all points of the given geometry
Intersection: Returns a geometric object that represents the intersecting parts of two given geometries
Union: Creates a geometric object that represents the combination of two given geometries
Difference: Returns the given geometries that do not intersect. If all gemetries intersect, an empty set will be returned.
Symmetric Difference: Creates a geometric object of the disjoint parts of two geometries. The output will have all pieceheld by one geometry or the other, but not the areas held by both.

Examples

Intersection
- All rivers within washington state boundary
- Residential areas with past landslide
Union
- Merging census data for two states in a single layer (Useful for studying phenomena that do not respect political boundaries)
- Merging state boundaries for Canada, U.S. and Mexico into a North American dataset (GADM makes this a breeze)
Buffer
- Instagram posts vs within 100m of a local restaurant
- Tweets vs within 1km of a football stadium
Convex Hull
- Bounding boxes, circles
- Range modeling for small data sets

Raster Functions

Slope - This function will calculate a slope surface given a raster holding an elevation model
Aspect - This outputs a surface holding values 0-360 referencing the azimuth of the given surface
Raster Calculator - Performs a designated mathematical equation on all values within a raster. This can also be used to combine/difference rasters.
Interpolation - Useful for resurfacing a dataset. This can also be used to create a continuous surface from a point dataset.
Reclassify - Useful for creating discrete value categories from continous values(e.g.float data) also useful for creating presence absence datasets.
Polygonize - Creates a set of polygon features representing the given raster dataset
Histogram - Create a histogram showing the distribution of values in a raster dataset

Exercise

We are going to utilize spatial functions to prepare data for the Landslide Exercise.

Import Washington boundary and dem_2927:
1. iRods access:
     /iplant/home/shared/aegis/Spatial-bootcamp/spatial-analysis/spatial-functions/washington.shp
  
  And:
     /iplant/home/shared/aegis/Spatial-bootcamp/spatial-analysis/spatial-functions/dem_2927.tif
  
  Or download here, unzip (washington.zip), and import:
     washington.zip
     dem_2927.tif
  
  You should now be viewing the boundary of Washington and a DEM of the US northwest:
Confirm both are in the same projection, EPSG:2927:

Notice how the two layers are aligned once they're imported.

Since we have not set our project projection ('on-the-fly' transformation is off) and the project projection has been defaulted to EPSG:2927 (see lower right corner of QGIS), that must mean both layers are stored with EPSG:2927.

Although, it's always recommended that you check projections of all layers.
Clip DEM to Washington boundary:
1. Open the raster Clipper tool: Menu Bar > Raster > Extraction > Clipper
  
  Configure inputs as follows:
  - Input file: dem_2927
  - Output file: wa_dem.tif
  - No data value: 0
  - Clipping mode: Mask Layer > washington
2. Remove washington.shp and dem_2927.tif and zoom into wa_dem.tif:
Create slope surface from wa_dem:
1. Open the raster DEM (Terrain models) tool: Menu Bar > Raster > Analysis > DEM (Terrain models)
  
  Configure inputs as follows:
  - Input file: wa_dem
  - Output file: wa_slope.tif
  - Band: 1
  - Mode: Slope
  - Scale: 0.30
  - Load into canvas when finished: (checked)
2. Your slope layer should look like the one below:
3. Create hillshade from wa_dem:
  1. - Open the DEM (Terrain models) tool and configure inputs as follows:
      - Input file: wa_dem
      - Output file: wa_hillshade.tif
      - Band: 1
      - Mode: Hillshade
      - Z factor: 1.00
      - Scale: 0.30
      - Azimuth of the light: 315.0
      - Altitude of the light: 45.0
      - Load into canvas when finished: (checked)
    - Your hillshade layer should look like the one below:
  You have just successfully clipped a raster to a vector, created a slope raster, and created a hillshade raster.
  
  The clipped DEM and slope with be used in the Landslide Susceptibility Model.
  
  The hillshade will be used in Compose a Map.
  1. SQL Simple Features Specification
  2. JTS
  3. Esri
  4. PostGIS Reference Manual. http://postgis.org/documentation/manual-svn/using_postigs_dbmanagement.html